3264 and All That
A Second Course in Algebraic Geometry
$115.00
 Authors:
 David Eisenbud, University of California, Berkeley
 Joe Harris, Harvard University, Massachusetts
 Date Published: April 2016
 availability: Available
 format: Hardback
 isbn: 9781107017085
$
115.00
Hardback
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This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenthcentury calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.
Read more Explores intersection theory  a central topic for everyone interested in algebraic geometry, from number theorists to theoretical physicists
 Ideal for graduate students and for individual mathematicians wishing to learn the ideas and techniques of algebraic geometry
 Contains more than 360 exercises with solutions available online
Reviews & endorsements
'… the book covers an important part of classical algebraic geometry with a modern point of view. It is indeed highly recommendable for a second (or a third) course in algebraic geometry and more generally, for every mathematician interested in concrete algebraic geometry.' Arnaud Beauville, MathSciNet
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×Product details
 Date Published: April 2016
 format: Hardback
 isbn: 9781107017085
 length: 603 pages
 dimensions: 260 x 182 x 37 mm
 weight: 1.29kg
 contains: 80 b/w illus. 360 exercises
 availability: Available
Table of Contents
Introduction
1. Introducing the Chow ring
2. First examples
3. Introduction to Grassmannians and lines in P3
4. Grassmannians in general
5. Chern classes
6. Lines on hypersurfaces
7. Singular elements of linear series
8. Compactifying parameter spaces
9. Projective bundles and their Chow rings
10. Segre classes and varieties of linear spaces
11. Contact problems
12. Porteous' formula
13. Excess intersections and the Chow ring of a blowup
14. The Grothendieck–Riemann–Roch theorem
Appendix A. The moving lemma
Appendix B. Direct images, cohomology and base change
Appendix C. Topology of algebraic varieties
Appendix D. Maps from curves to projective space
References
Index.
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